Exact Single Spin Flip for the Hubbard Model in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">d</mml:mi><mml:mspace/><mml:mo>=</mml:mo><mml:mspace/><mml:mi>∞</mml:mi></mml:math>

Uhrig, Götz S.

doi:10.1103/physrevlett.77.3629

Cited by 24 publications

(56 citation statements)

References 41 publications

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“…This approach reduces the extensive lattice problem to a selfconsistency problem involving a single-impurity Anderson model (SIAM) [1]. The latter can be viewed as an interacting site coupled to a semi-infinite chain of non-interacting fermions [13,14] which is solved by dynamic density-matrix renormalization (D-DMRG) [15,16]. This combination of D-DMRG and DMFT represents a powerful tool for investigating the T = 0 one- particle propagators of interacting lattice models [17][18][19][20] Its particular merit is to have a well-controlled energy resolution over the whole energy range [15,21].…”

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confidence: 99%

Emergent Collective Modes and Kinks in Electronic Dispersions

2009

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Recently, it was shown that strongly correlated metallic fermionic systems [Nature Phys. 3, 168 (2007)] generically display kinks in the dispersion of single fermions without the coupling to collective modes. Here we provide compelling evidence that the physical origin of these kinks are emerging internal collective modes of the fermionic systems. In the Hubbard model under study these modes are identified to be spin fluctuations which are the precursors of the spin excitations in the insulating phase. In spite of their damping the emergent modes give rise to signatures very similar to features of models including coupling to external modes. PACS numbers: 71.27.+a,71.30.+h,74.25.Jb,75.20.Hr The description of nascent collective modes which emerge from elementary excitations on varying a control parameter g is an intensely studied field of research. The difficulty relies in the fact that in one limit of g the elementary excitations dominate while in the other limit the collective modes dominate. In the vicinity of the transition or around the crossover necessarily both degrees of freedom need to be taken into account so that the interplay of both kinds of excitations is crucial. No simple theory assesses this interplay.Here we will focus on strongly correlated electronic systems and especially on the metal-insulator transition induced by a repulsive interaction U on a lattice with a commensurate number of electrons per site. The simplest case is a local interaction with one electron per site on average [1]. For low values of U the electrons move through the lattice so that the system is metallic. For large values of U the hopping is blocked and the system is insulating with frozen charge degree of freedom. But the spin dynamics is still active. In leading order in t/U (t the hopping matrix element) this dynamics is captured by a Heisenberg model [2]. The collective modes are the spin excitations built from bound electron-hole pairs.When the system is still metallic, but close to its insulating regime, we intend to understand how the emergent spin modes influence the electronic quasiparticles. This issue is important to many strongly correlated systems. One prominent example is high temperature superconductiviy where a large number of theories explains the attractive interaction between charge carriers by the interplay with spin fluctuations. One line of argument links the kinks that are observed in the dispersion of the fermionic holes, see for instance [3,4,5,6,7], to the interaction with bosonic modes. This is the usual reasoning for phonons coupled to electrons [8]. Other bosonic modes, however, will engender the same sort of kinks, for instance plasmons [9]. In the high-T c materials, spin fluctuations have an important influence on the quasiparticles, see e.g. Ref.[10]. They are likely candidates for the bosonic modes, see e.g. Ref.[11] where this is worked out in the fluctuation-exchange approximation.Byczuk et al. [12] recently showed by a sophisticated analysis of the equations of dynamic mean-field t...

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Emergent Collective Modes and Kinks in Electronic Dispersions

2009

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“…Compared to this, relatively little effort is concentrated on the search for magnetic solutions of the Hubbard model. Some interesting recent investigations which address the magnetic behaviour can be found in [17][18][19][20][21] . Ferromagnetic solutions are to be expected, if at all, only in the strong coupling regime U/W > 1 (W: Blochbandwidth).…”

Section: Introductionmentioning

confidence: 99%

Magnetism in the single-band Hubbard model

Herrmann

Nolting

1997

Journal of Magnetism and Magnetic Materials

128

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A self-consistent spectral density approach (SDA) is applied to the Hubbard model to investigate the possibility of spontaneous ferro-and antiferromagnetism. Starting point is a two-pole ansatz for the single-electron spectral density, the free parameter of which can be interpreted as energies and spectral weights of respective quasiparticle excitations. They are determined by fitting exactly calculated spectral moments. The resulting self-energy consists of a local and a non-local part. The higher correlation functions entering the spin-dependent local part can be expressed as functionals of the single-electron spectral density. Under certain conditions for the decisive model parameters (Coulomb interaction U , Bloch-bandwidth W , band occupation n, temperature T ) the local part of the self-energy gives rise to a spin-dependent band shift, thus allowing for spontaneous band magnetism. As a function of temperature, second order phase transitions are found away from half filling, but close to half filling the system exhibits a tendency towards first order transitions. The non-local self-energy part is determined by use of proper two-particle spectral densities. Its main influence concerns a (possibly spin-dependent) narrowing of the quasiparticle bands with the tendency to stabilize magnetic solutions. The non-local self-energy part disappears in the limit of infinite dimensions. We present a full evaluation of the Hubbard model in terms of quasiparticle densities of states, quasiparticle dispersions, magnetic phase diagram, critical temperatures (TC , TN ) as well as spin and particle correlation functions. Special attention is focused on the non-locality of the electronic self-energy, for which some rigorous limiting cases are worked out.

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“…They were made possible mainly by the development (i) of new analytic approaches, such as the mathematical methods used to investigate flat-band ferromagnetism [6] and its extensions [14,15] as well as dynamical mean-field theory (DMFT) [16,17,18], (ii) of new numerical techniques, such as the density matrix renormalization group (DMRG) which yields precise results in d = 1 [19], and (iii) of new comprehensive approximation schemes such as the multiband Gutzwiller wave function [20], or the new ab initio computational scheme LDA+DMFT [21,22,23] which merges conventional band structure theory (LDA) with a comprehensive many-body technique (DMFT).…”

Section: Introductionmentioning

confidence: 99%

Metallic Ferromagnetism — An Electronic Correlation Phenomenon

Vollhardt

Blümer

Held

et al. 2001

Band-Ferromagnetism

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Abstract. New insights into the microscopic origin of itinerant ferromagnetism were recently gained from investigations of electronic lattice models within dynamical meanfield theory (DMFT). In particular, it is now established that even in the one-band Hubbard model metallic ferromagnetism is stable at intermediate values of the interaction U and density n on regular, frustrated lattices. Furthermore, band degeneracy along with Hund's rule couplings is very effective in stabilizing metallic ferromagnetism in a broad range of electron fillings. DMFT also permits one to investigate more complicated correlation models, e.g., the ferromagnetic Kondo lattice model with Coulomb interaction, describing electrons in manganites with perovskite structure. Here we review recent results obtained with DMFT which help to clarify the origin of band-ferromagnetism as a correlation phenomenon.

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Exact Single Spin Flip for the Hubbard Model ind=∞

Cited by 24 publications

References 41 publications

Emergent Collective Modes and Kinks in Electronic Dispersions

Emergent Collective Modes and Kinks in Electronic Dispersions

Magnetism in the single-band Hubbard model

Metallic Ferromagnetism — An Electronic Correlation Phenomenon

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